Calculating Max Compression of Massless Hookslaw Spring

[joemama69]

Homework Statement

A massless hooksw law spring has a unstretched length of L, when a mass m is ploaced on it, and slowly lowered until the mass is at rest, the spring is queezed to a length of x. the mass is then dropped on the spring from a height of h, use energ methods

what is the length of the spring at maximum compression as a result of the mass dropping on it

Homework Equations

The Attempt at a Solution

mgh = -mgs + .5ks²

s = -mg + or -(((mg)² - 4(.5k)(mgh))/k)^.5

if this is correct

 

[flatmaster]

The question is worded aquardly, but I think you're on the right path with your firse equation. Now you need to write the spring constant k in terms of other parameters you have in your problem.

Also, you get two anilytical solutions. Can you think which sollution is correct? What does your non-physical solution correspond do?

 

[joemama69]

what would be the benefit from solving for the spring constant

it asks for the length of the spring at compression s

 

[jgens]

what would be the benefit from solving for the spring constant

That way the spring constant is expressed in terms of other known parameters.

 

[joemama69]

k = (2mgs - 2mgh)s² = 2mg(s-h)/s²

i still don't understand how that helps, what would i use it for now